The Modified Stochastic Games

TL;DR

This paper introduces the modified game, a new analytical tool for multiplayer stochastic games, enabling the study of equilibria and value properties, and proving the existence of uniform equilibria under certain conditions.

Contribution

It presents the modified game as a novel approach to analyze multiplayer stochastic games, linking game parameters to equilibrium existence.

Findings

The modified game depends on discount factor, initial state, and state partitions.

Properties like equilibria, min-max, and max-min values are studied.

Used to prove the existence of uniform equilibrium in specific multiplayer stochastic games.

Abstract

We present a new tool for the study of multiplayer stochastic games, namely the modified game, which is a normal-form game that depends on the discount factor, the initial state, and for every player a partition of the set of states and a vector that assigns a real number to each element of the partition. We study properties of the modified game, like its equilibria, min-max value, and max-min value. We then show how this tool can be used to prove the existence of a uniform equilibrium in a certain class of multiplayer stochastic games.